Grader Position &
Proposed Problems for Additional Project Options
Applications for Grader postions for this course
preferably submitted by Friday Aug 31. It is OK
to be a current student in the class.
Several (non PHD students) have proposed to
do new
CEE 509/CS 5722/ORIE 5340 Heuristic Methods for Optimization
Homework 7: Markov Chains (Theory homework)
Students taking the class for 3 credits with the project and without theory can skip this
homework.
Assigned: Saturday, October 13, 2012
Due: Friday,
CEE 509/CS 5722/ORIE 5340 Heuristic Methods for Optimization
Homework 8: Markov Chains and Schema Theorem
Students taking the class for 3 credits with the project and without theory can skip this
homework.
Assigned: Friday, Oct 19, 2012
Due: Friday, Oct 2
CEE 5290/COM S 5722/ORIE 5340 Heuristic Methods for Optimization
Homework 9: No Free Lunch Theorem
(Homework only for students taking the Theory part of the course.)
Assigned: Oct. 27, 2012
Due:Nov. 2, 2012 (automatic extension to Nov. 5 if you wish)
TA O
CEE 5290/COM S 5722/ORIE 5340 Heuristic Methods for Optimization
Homework 2: Simulated Annealing
Assigned: Friday, September 5, 2014
Due: Friday, September 12, 2014 @ noon
IMPORTANT: In the interest of being able to answer everyones questions on the HW pr
CEE 5290/CS 5722/ORIE 5340 Heuristic Methods for Optimization
Homework 4: Tabu Search
Assigned: Fri, September 19th, 2014
Due: Fri, September 26th, 2014
1. (Computer Code) Assume that you want to find the maximum of the polynomial
F(x)=x3-60x2 +90x , 0<x<
CEE 5290/CS 5722/ORIE 5340: Heuristic Methods for Optimization
Homework 3: Binary Genetic Algorithm
Assigned: Monday, September 10, 2012
Due: Wednesday, September 19, 2012
1. If you wish to improve any of the basic approaches specified by the GA then feel
Projects and Decisions
If you do an existing project (one of five announced on
the syllabus), you do not need to decide for several
weeks about which project you want to do.
We will have outside speakers to describe the exisiting
projects, You can decid
What happens if T1 is decreased to T2 and Cost does
not change?
8-31-12
1
Nature of Improvement Step In SA
Hence the more uphill the move (as
measured by !COST = [COST(NewS)COST(CurS)], the smaller the probability.
Also the larger the temperature T, the
Overall Allocation of Evaluations
You will want to apportion your evaluations over
parameter setting, and almost greedy search as
well as for regular SA
Est parameters
Start of SA algorithm
AP
Numbers of Cost evaluations
Maxiter=GM, Total Evals=AP+GM+E
To
Genetic Algorithms
Probably the Most Popular Heuristic Algorithm
(but not necessarily the best for some applications)
Handout 9-7-12
1
Genetic Algorithms
The heuristic search method Genetic Algorithms is
inspired by the mechanism Nature uses to improve
p
1
Method 2 Revised: Estimating To by doing
AP extra evaluations of Cost(S)
Pick an Sp and evaluate Cost(Sm) for Sm ! Q m=1,
,AP where the Sm are chosen at random. (User
chooses Sp , the definition of Q and N(S) and how
large AP is).
One possible choice fo
Iteration 2
We dont pick best solution (1,3)
because it is Tabu and because the
solution value with that swap 16
(=18+(-2) is not as good as other
Scurr found already.
1
Iteration 2
We do pick swap (2,4) since it is the
best non tabu move.
2
Iteration 3 :
CS 5722/CEE 5290/ORIE 5340
Heuristic Methods for Optimization
Homework 1: Algorithms, Complexity, and Randomized Search
Assigned: Friday , August 24 2012
Due: Friday , August 31, 2012 (Students entering the course late or otherwise needing extra time
for
CEE 5290/COM S 5722/ORIE 5340 Heuristic Methods for Optimization
Homework 2: Simulated Annealing
Assigned: Saturday, September 1, 2012
Due: Monday, September 10, 2012
IMPORTANT: In the interest of being able to answer everyones questions on the HW promptl
CS 5722/CEE 5290/ORIE 5340
Heuristic Methods for Optimization
Homework 1: Algorithms, Complexity, and Randomized Search
Assigned: Wednesday , August 27, 2014
Due: Friday Sept.5 Students entering the course late or otherwise needing extra time for the firs
HW1 Solutions
Total points possible: 20
Simple optimization algorithms: We wish to minimize the following simple onedimensional cost function:
Costs(s) = (400 (s 21)2) * sin(s*pi/6)
Constraints: s integer-valued, 0 s 500
Part(a): (2 points)
Write a MATLAB
CEE 5290/CS 5722/ORIE 5340: Heuristic Methods for Optimization
Homework 3: Binary Genetic Algorithm
Assigned: Friday, September 12, 2014
Due: Friday, September 19, 2014 @ noon (free extension to Monday, Sep. 22 @noon)
1. If you wish to improve any of the
Permutation Variables and Traveling
Salesman Problem
Permutation an ordered list of the numbers 1 to N.
Hence a different order is a different value of the variable
(e.g. (1 2 3) is different from (2 1 3)
The classical permutation problem is the traveli
Application of Cycling to the
permutation (layering) Problem
How many members in set of all possible
permutations of 7 numbers?_
How many members in set of all possible
perturbation by all possible pairwise
swap_?
9-19-14
1
How could you create a cycle
Review
In last lecture we discussed how to use Genetic
Algorithm with Real Variables.
We discussed two possibilities:
Use real coded GA
Use binary coded GA by
discretize the real numbers
Convert the discrete numbers into binary strings
Solve the bi
Mutation for Real-Valued Genetic Algorithms
Mutation refers to creation of a new solution from one
and only one parent. (Otherwise the creation is referred
to as a recombination.) There are many ways that this
can be done. Let x be the mutation of x.
Fo
Constraint Handling in GAs
The following slides on constraint handling
are based on an excellent paper by Deb
(2000)
Constraint handling techniques are classed
into 5 methods:
1. Based on preserving feasibility of solutions
2. Based on penalty functions
Tabu* Search
* Tabu = Taboo
1
Tabu = Forbidden
2
Tabu Search
Tabu Search (TS) algorithm is based on the idea that
you want to prevent the search from going back to
some regions.
Tabu means forbidden.
Comments & Corrections on Real Valued
Tabu Search
How do we use Tabu Search for decision
vectors that are real valued (e.g. not binary
strings, permutations or integer vectors)?
This is a new section, and I want to redo some of
the notes on this section
Genetics and Genetic Algorithms
Nuclaic acids
carrying
genetic
information
9-10-14
We are all
interested in
our own
genetics so
perhaps that
is one of the
reasons
Genetic
Algorithms
are so
popular.
1
Genetic Algorithms
The heuristic search method Genetic